• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.61-66
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• 1984

It is well-known that the most interesting non-integrable almost Hermitian manifold are the nearly Kaehlerian manifolds ([2] and [3]), and that there exists a complex but not a Kaehlerian structure on Riemannian product manifolds of two normal contact manifolds [4]. The purpose of the present paper is to study nearly Kaehlerian product manifolds of two almost contact metric manifolds and investigate the geometrical structures of these manifolds. Unless otherwise stated, we shall always assume that manifolds and quantities are differentiable of class $C^{\infty}$. In Paragraph 1, we give brief discussions of almost contact metric manifolds and their Riemannian product manifolds. In paragraph 2, we investigate the perfect conditions for Riemannian product manifolds of two almost contact metric manifolds to be nearly Kaehlerian and the non-existence of a nearly Kaehlerian product manifold of contact metric manifolds. Paragraph 3 will be devoted to a proof of the following; A conformally flat compact nearly Kaehlerian product manifold of two almost contact metric manifolds is isomatric to a Riemannian product manifold of a complex projective space and a flat Kaehlerian manifold..

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.935-951
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• 2020

The aim of the paper is to study some geometric properties of weakly Z-symmetric manifolds. Weakly Z-symmetric manifolds with Codazzi type and cyclic parallel Z tensor are studied. We consider Einstein weakly Z-symmetric manifolds and conformally flat weakly Z-symmetric manifolds. Next, it is shown that a totally umbilical hypersurface of a conformally flat weakly Z-symmetric manifolds is of quasi constant curvature. Also, decomposable weakly Z-symmetric manifolds are studied and some examples are constructed to support the existence of such manifolds.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.753-771
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• 2015

A complete invariant defined for (closed connected orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold itself can be reconstructed from the data of the complete invariant, then it is called a characteristic invariant defined for the 3-manifolds. In a previous work, a characteristic lattice point invariant defined for the 3-manifolds was constructed by using an embedding of the prime links into the set of lattice points. In this paper, a characteristic rational invariant defined for the 3-manifolds called the characteristic genus defined for the 3-manifolds is constructed by using an embedding of a set of lattice points called the PDelta set into the set of rational numbers. The characteristic genus defined for the 3-manifolds is also compared with the Heegaard genus, the bridge genus and the braid genus defined for the 3-manifolds. By using this characteristic rational invariant defined for the 3-manifolds, a smooth real function with the definition interval (-1, 1) called the characteristic genus function is constructed as a characteristic invariant defined for the 3-manifolds.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.699-714
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• 2014

The object of the present paper is to study almost pseudo conharmonically symmetric manifolds. Some geometric properties of almost pseudo conharmonically symmetric manifolds have been studied under certain curvature conditions. Finally, we give three examples of almost pseudo conharmonically symmetric manifolds.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.85-97
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• 2017

We classify Kenmotsu 3-manifolds and cosymplectic 3-manifolds with ${\eta}-parallel$ Ricci operator.

• East Asian mathematical journal
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• v.18 no.2
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• pp.235-243
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• 2002

In this paper, we get conditions for the natural projections of some product manifolds with varying metrics of two Riemannian manifolds to be harmonic, and necessary and sufficient conditions for some product manifolds with the harmonic natural projections of two Einstein manifolds to be Einstein manifolds.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.539-545
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• 2021

In this paper, we study some symmetric and recurrent conditions of nearly cosymplectic manifolds. We prove that Ricci-semisymmetric and Ricci-recurrent nearly cosymplectic manifolds are Einstein and conformal flat nearly cosymplectic manifold is locally isometric to Riemannian product ℝ × N, where N is a nearly Kähler manifold.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.505-521
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• 2010

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.62-77
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• 2022

This study presents an 𝛼-Sasakian structure on the product manifold M₁ × 𝛽(I), where M₁ is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.507-516
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• 2017

Real Bott manifolds is a class of flat manifolds with holonomy group $\mathbb{Z}^k_2$ of diagonal type. In this paper we formulate necessary and sufficient conditions of the existence of a Spin-structure on real Bott manifolds. It extends results of [9].